Abstract

Sinusoidal fringe pattern is widely used in optical profilometry; however, the traditional constant-frequency sinusoidal fringe pattern reduces 3D measurement accuracy in the defocus region. To this end, this paper presents a variable-frequency sinusoidal fringe pattern method that is optimized by the measurement depth. The proposed method improves the pixel matching accuracy and thus increases measurement accuracy. This paper theoretically determines the optimal frequency by analyzing the pixel matching error caused by intense noise in a captured image; presents the online frequency optimization along abscissa and ordinate axes in the sinusoidal fringe patterns; and details the encoding and decoding to use variable-frequency fringe patterns for 3D profilometry. Simulations and experiments demonstrate that our proposed method can improve the 3D measurement accuracy and increase measurement robustness.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Profilometry without phase unwrapping using multi-frequency and four-step phase-shift sinusoidal fringe projection

Eun-Hee Kim, Joonku Hahn, Hwi Kim, and Byoungho Lee
Opt. Express 17(10) 7818-7830 (2009)

Suppression of projector distortion in phase-measuring profilometry by projecting adaptive fringe patterns

Junzheng Peng, Xiaoli Liu, Dingnan Deng, Hongwei Guo, Zewei Cai, and Xiang Peng
Opt. Express 24(19) 21846-21860 (2016)

Determination and adjustment of optimal defocus level for fringe projection systems

Bingbing Han, Shourui Yang, and Shengyong Chen
Appl. Opt. 58(23) 6300-6307 (2019)

References

  • View by:
  • |
  • |
  • |

  1. L. Zhou, F. Zhou, D. Qu, X. Liu, and W. Lu, “Error analysis of the non-diffraction grating structured light generated by triangular prism,” Opt. Commun. 306, 174–178 (2013).
    [Crossref]
  2. P. Jin, J. Liu, S. Liu, and X. Wang, “A new multi-vision-based reconstruction algorithm for tube inspection,” Int. J. Adv. Manuf. Technol. 93, 1–15 (2017).
    [Crossref]
  3. Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3d shape and colour texture of moving objects using ir and colour fringe projection techniques,” Opt. & Lasers Eng. 61, 1–7 (2014).
    [Crossref]
  4. J. Geng, “Structured-light 3d surface imaging: a tutorial,” Adv. Opt. Photonics 3, 128–160 (2011).
    [Crossref]
  5. J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern recognition 43, 2666–2680 (2010).
    [Crossref]
  6. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
    [Crossref]
  7. E. Li, X. Peng, J. Xi, J. Chicharo, J. Yao, and D. Zhang, “Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3d profilometry,” Opt. Express 13, 1561–1569 (2005).
    [Crossref]
  8. Y. Y. Cheng and J. C. Wyant, “Multiple-wavelength phase-shifting interferometry,” Appl. Opt. 24, 804–807 (1985).
    [Crossref]
  9. Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
    [Crossref]
  10. Y. Wang and S. Zhang, “Three-dimensional shape measurement with binary dithered patterns,” Appl. Opt. 51, 6631–6636 (2012).
    [Crossref]
  11. W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
    [Crossref]
  12. J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3d shape measurement,” Opt. Lasers Eng. 51, 790–795 (2013).
    [Crossref]
  13. J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).
    [Crossref]
  14. J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
    [Crossref]
  15. X. X. Li, Z. J. Zhang, and C. Yang, “High-quality fringe pattern generation using binary pattern optimization based on a novel objective function,” Optik - Int. J. for Light. Electron Opt. 127, 5322–5327 (2016).
    [Crossref]
  16. G. A. Ayubi, J. A. Ayubi, J. M. D. Martino, and J. A. Ferrari, “Pulse-width modulation in defocused three-dimensional fringe projection,” Opt. Lett. 35, 3682–3684 (2010).
    [Crossref] [PubMed]
  17. Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
    [Crossref]
  18. M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15, 119–132 (2011).
    [Crossref]
  19. Y. Oyamada and H. Saito, “Estimation of projector defocus blur by extracting texture rich region in projection image,” Vaclav Skala - UNION Agency (2008).
  20. Y. Oyamada and H. Saito, “Defocus blur correcting projector-camera system,” Lect. Notes Comput. Sci. 5259, 453–464 (2008).
    [Crossref]
  21. K. Irie, A. E. Mckinnon, K. Unsworth, and I. M. Woodhead, “A technique for evaluation of ccd video-camera noise,” IEEE Transactions on Circuits Syst. for Video Technol. 18, 280–284 (2008).
    [Crossref]
  22. Y. Oyamada and H. Saito, “Focal pre-correction of projected image for deblurring screen image,” Comput. Vis. Pattern Recognition, 2007. CVPR ’07. IEEE Conf. on., 1–8 (2007).
  23. S. Zhuo and T. Sim, “Defocus map estimation from a single image,” Pattern Recognit. 44, 1852–1858 (2011).
    [Crossref]
  24. H. Chen, J. Su, J. Xu, K. Chen, R. Chen, and Z. Zhang, “Accurate calibration method for camera and projector in fringe patterns measurement system,” Appl. Opt. 55, 4293–4300 (2016).
    [Crossref]

2017 (1)

P. Jin, J. Liu, S. Liu, and X. Wang, “A new multi-vision-based reconstruction algorithm for tube inspection,” Int. J. Adv. Manuf. Technol. 93, 1–15 (2017).
[Crossref]

2016 (2)

X. X. Li, Z. J. Zhang, and C. Yang, “High-quality fringe pattern generation using binary pattern optimization based on a novel objective function,” Optik - Int. J. for Light. Electron Opt. 127, 5322–5327 (2016).
[Crossref]

H. Chen, J. Su, J. Xu, K. Chen, R. Chen, and Z. Zhang, “Accurate calibration method for camera and projector in fringe patterns measurement system,” Appl. Opt. 55, 4293–4300 (2016).
[Crossref]

2014 (3)

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).
[Crossref]

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3d shape and colour texture of moving objects using ir and colour fringe projection techniques,” Opt. & Lasers Eng. 61, 1–7 (2014).
[Crossref]

2013 (3)

L. Zhou, F. Zhou, D. Qu, X. Liu, and W. Lu, “Error analysis of the non-diffraction grating structured light generated by triangular prism,” Opt. Commun. 306, 174–178 (2013).
[Crossref]

W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
[Crossref]

J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3d shape measurement,” Opt. Lasers Eng. 51, 790–795 (2013).
[Crossref]

2012 (1)

2011 (3)

S. Zhuo and T. Sim, “Defocus map estimation from a single image,” Pattern Recognit. 44, 1852–1858 (2011).
[Crossref]

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15, 119–132 (2011).
[Crossref]

J. Geng, “Structured-light 3d surface imaging: a tutorial,” Adv. Opt. Photonics 3, 128–160 (2011).
[Crossref]

2010 (2)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern recognition 43, 2666–2680 (2010).
[Crossref]

G. A. Ayubi, J. A. Ayubi, J. M. D. Martino, and J. A. Ferrari, “Pulse-width modulation in defocused three-dimensional fringe projection,” Opt. Lett. 35, 3682–3684 (2010).
[Crossref] [PubMed]

2008 (2)

Y. Oyamada and H. Saito, “Defocus blur correcting projector-camera system,” Lect. Notes Comput. Sci. 5259, 453–464 (2008).
[Crossref]

K. Irie, A. E. Mckinnon, K. Unsworth, and I. M. Woodhead, “A technique for evaluation of ccd video-camera noise,” IEEE Transactions on Circuits Syst. for Video Technol. 18, 280–284 (2008).
[Crossref]

2006 (2)

Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
[Crossref]

Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
[Crossref]

2005 (1)

2004 (1)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[Crossref]

1985 (1)

Ayubi, G. A.

Ayubi, J. A.

Chen, C.

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3d shape and colour texture of moving objects using ir and colour fringe projection techniques,” Opt. & Lasers Eng. 61, 1–7 (2014).
[Crossref]

Chen, H.

Chen, K.

Chen, R.

Chen, W.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[Crossref]

Cheng, Y. Y.

Chicharo, J.

Dai, J.

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).
[Crossref]

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3d shape measurement,” Opt. Lasers Eng. 51, 790–795 (2013).
[Crossref]

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern recognition 43, 2666–2680 (2010).
[Crossref]

Ferrari, J. A.

Geng, J.

J. Geng, “Structured-light 3d surface imaging: a tutorial,” Adv. Opt. Photonics 3, 128–160 (2011).
[Crossref]

Huang, S. J.

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3d shape and colour texture of moving objects using ir and colour fringe projection techniques,” Opt. & Lasers Eng. 61, 1–7 (2014).
[Crossref]

Irie, K.

K. Irie, A. E. Mckinnon, K. Unsworth, and I. M. Woodhead, “A technique for evaluation of ccd video-camera noise,” IEEE Transactions on Circuits Syst. for Video Technol. 18, 280–284 (2008).
[Crossref]

Iwai, D.

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15, 119–132 (2011).
[Crossref]

Jin, P.

P. Jin, J. Liu, S. Liu, and X. Wang, “A new multi-vision-based reconstruction algorithm for tube inspection,” Int. J. Adv. Manuf. Technol. 93, 1–15 (2017).
[Crossref]

Li, B.

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).
[Crossref]

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

Li, E.

Li, X. X.

X. X. Li, Z. J. Zhang, and C. Yang, “High-quality fringe pattern generation using binary pattern optimization based on a novel objective function,” Optik - Int. J. for Light. Electron Opt. 127, 5322–5327 (2016).
[Crossref]

Li, Z.

Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
[Crossref]

Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
[Crossref]

Liu, J.

P. Jin, J. Liu, S. Liu, and X. Wang, “A new multi-vision-based reconstruction algorithm for tube inspection,” Int. J. Adv. Manuf. Technol. 93, 1–15 (2017).
[Crossref]

Liu, S.

P. Jin, J. Liu, S. Liu, and X. Wang, “A new multi-vision-based reconstruction algorithm for tube inspection,” Int. J. Adv. Manuf. Technol. 93, 1–15 (2017).
[Crossref]

Liu, X.

L. Zhou, F. Zhou, D. Qu, X. Liu, and W. Lu, “Error analysis of the non-diffraction grating structured light generated by triangular prism,” Opt. Commun. 306, 174–178 (2013).
[Crossref]

Llado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern recognition 43, 2666–2680 (2010).
[Crossref]

Lohry, W.

Lu, W.

L. Zhou, F. Zhou, D. Qu, X. Liu, and W. Lu, “Error analysis of the non-diffraction grating structured light generated by triangular prism,” Opt. Commun. 306, 174–178 (2013).
[Crossref]

Martino, J. M. D.

Mckinnon, A. E.

K. Irie, A. E. Mckinnon, K. Unsworth, and I. M. Woodhead, “A technique for evaluation of ccd video-camera noise,” IEEE Transactions on Circuits Syst. for Video Technol. 18, 280–284 (2008).
[Crossref]

Nagase, M.

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15, 119–132 (2011).
[Crossref]

Nayar, S.

Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
[Crossref]

Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
[Crossref]

Oyamada, Y.

Y. Oyamada and H. Saito, “Defocus blur correcting projector-camera system,” Lect. Notes Comput. Sci. 5259, 453–464 (2008).
[Crossref]

Y. Oyamada and H. Saito, “Focal pre-correction of projected image for deblurring screen image,” Comput. Vis. Pattern Recognition, 2007. CVPR ’07. IEEE Conf. on., 1–8 (2007).

Y. Oyamada and H. Saito, “Estimation of projector defocus blur by extracting texture rich region in projection image,” Vaclav Skala - UNION Agency (2008).

Peng, X.

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern recognition 43, 2666–2680 (2010).
[Crossref]

Qu, D.

L. Zhou, F. Zhou, D. Qu, X. Liu, and W. Lu, “Error analysis of the non-diffraction grating structured light generated by triangular prism,” Opt. Commun. 306, 174–178 (2013).
[Crossref]

Saito, H.

Y. Oyamada and H. Saito, “Defocus blur correcting projector-camera system,” Lect. Notes Comput. Sci. 5259, 453–464 (2008).
[Crossref]

Y. Oyamada and H. Saito, “Focal pre-correction of projected image for deblurring screen image,” Comput. Vis. Pattern Recognition, 2007. CVPR ’07. IEEE Conf. on., 1–8 (2007).

Y. Oyamada and H. Saito, “Estimation of projector defocus blur by extracting texture rich region in projection image,” Vaclav Skala - UNION Agency (2008).

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern recognition 43, 2666–2680 (2010).
[Crossref]

Sato, K.

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15, 119–132 (2011).
[Crossref]

Sim, T.

S. Zhuo and T. Sim, “Defocus map estimation from a single image,” Pattern Recognit. 44, 1852–1858 (2011).
[Crossref]

Su, J.

Su, X.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[Crossref]

Unsworth, K.

K. Irie, A. E. Mckinnon, K. Unsworth, and I. M. Woodhead, “A technique for evaluation of ccd video-camera noise,” IEEE Transactions on Circuits Syst. for Video Technol. 18, 280–284 (2008).
[Crossref]

Wang, X.

P. Jin, J. Liu, S. Liu, and X. Wang, “A new multi-vision-based reconstruction algorithm for tube inspection,” Int. J. Adv. Manuf. Technol. 93, 1–15 (2017).
[Crossref]

Wang, Y.

Woodhead, I. M.

K. Irie, A. E. Mckinnon, K. Unsworth, and I. M. Woodhead, “A technique for evaluation of ccd video-camera noise,” IEEE Transactions on Circuits Syst. for Video Technol. 18, 280–284 (2008).
[Crossref]

Wyant, J. C.

Xi, J.

Xu, J.

Xu, Y. J.

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3d shape and colour texture of moving objects using ir and colour fringe projection techniques,” Opt. & Lasers Eng. 61, 1–7 (2014).
[Crossref]

Yang, C.

X. X. Li, Z. J. Zhang, and C. Yang, “High-quality fringe pattern generation using binary pattern optimization based on a novel objective function,” Optik - Int. J. for Light. Electron Opt. 127, 5322–5327 (2016).
[Crossref]

Yao, J.

Zhang, D.

Zhang, S.

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).
[Crossref]

J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3d shape measurement,” Opt. Lasers Eng. 51, 790–795 (2013).
[Crossref]

W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
[Crossref]

Y. Wang and S. Zhang, “Three-dimensional shape measurement with binary dithered patterns,” Appl. Opt. 51, 6631–6636 (2012).
[Crossref]

Zhang, Z.

Zhang, Z. H.

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3d shape and colour texture of moving objects using ir and colour fringe projection techniques,” Opt. & Lasers Eng. 61, 1–7 (2014).
[Crossref]

Zhang, Z. J.

X. X. Li, Z. J. Zhang, and C. Yang, “High-quality fringe pattern generation using binary pattern optimization based on a novel objective function,” Optik - Int. J. for Light. Electron Opt. 127, 5322–5327 (2016).
[Crossref]

Zhou, F.

L. Zhou, F. Zhou, D. Qu, X. Liu, and W. Lu, “Error analysis of the non-diffraction grating structured light generated by triangular prism,” Opt. Commun. 306, 174–178 (2013).
[Crossref]

Zhou, L.

L. Zhou, F. Zhou, D. Qu, X. Liu, and W. Lu, “Error analysis of the non-diffraction grating structured light generated by triangular prism,” Opt. Commun. 306, 174–178 (2013).
[Crossref]

Zhuo, S.

S. Zhuo and T. Sim, “Defocus map estimation from a single image,” Pattern Recognit. 44, 1852–1858 (2011).
[Crossref]

ACM Transactions on Graph. (TOG) (2)

Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
[Crossref]

Z. Li and S. Nayar, “Projection defocus analysis for scene capture and image display,” ACM Transactions on Graph. (TOG) 25, 907–915 (2006).
[Crossref]

Adv. Opt. Photonics (1)

J. Geng, “Structured-light 3d surface imaging: a tutorial,” Adv. Opt. Photonics 3, 128–160 (2011).
[Crossref]

Appl. Opt. (3)

IEEE Transactions on Circuits Syst. for Video Technol. (1)

K. Irie, A. E. Mckinnon, K. Unsworth, and I. M. Woodhead, “A technique for evaluation of ccd video-camera noise,” IEEE Transactions on Circuits Syst. for Video Technol. 18, 280–284 (2008).
[Crossref]

Int. J. Adv. Manuf. Technol. (1)

P. Jin, J. Liu, S. Liu, and X. Wang, “A new multi-vision-based reconstruction algorithm for tube inspection,” Int. J. Adv. Manuf. Technol. 93, 1–15 (2017).
[Crossref]

Lect. Notes Comput. Sci. (1)

Y. Oyamada and H. Saito, “Defocus blur correcting projector-camera system,” Lect. Notes Comput. Sci. 5259, 453–464 (2008).
[Crossref]

Opt. & Lasers Eng. (1)

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3d shape and colour texture of moving objects using ir and colour fringe projection techniques,” Opt. & Lasers Eng. 61, 1–7 (2014).
[Crossref]

Opt. Commun. (1)

L. Zhou, F. Zhou, D. Qu, X. Liu, and W. Lu, “Error analysis of the non-diffraction grating structured light generated by triangular prism,” Opt. Commun. 306, 174–178 (2013).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (4)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[Crossref]

J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3d shape measurement,” Opt. Lasers Eng. 51, 790–795 (2013).
[Crossref]

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).
[Crossref]

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

Opt. Lett. (2)

Optik - Int. J. for Light. Electron Opt. (1)

X. X. Li, Z. J. Zhang, and C. Yang, “High-quality fringe pattern generation using binary pattern optimization based on a novel objective function,” Optik - Int. J. for Light. Electron Opt. 127, 5322–5327 (2016).
[Crossref]

Pattern Recognit. (1)

S. Zhuo and T. Sim, “Defocus map estimation from a single image,” Pattern Recognit. 44, 1852–1858 (2011).
[Crossref]

Pattern recognition (1)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern recognition 43, 2666–2680 (2010).
[Crossref]

Virtual Real. (1)

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15, 119–132 (2011).
[Crossref]

Other (2)

Y. Oyamada and H. Saito, “Estimation of projector defocus blur by extracting texture rich region in projection image,” Vaclav Skala - UNION Agency (2008).

Y. Oyamada and H. Saito, “Focal pre-correction of projected image for deblurring screen image,” Comput. Vis. Pattern Recognition, 2007. CVPR ’07. IEEE Conf. on., 1–8 (2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (21)

Fig. 1
Fig. 1 Interactive influence of frequency of sinusoidal fringes and noise on pixel matching accuracy.
Fig. 2
Fig. 2 Geometric optics model:(a)projector; (b)camera.
Fig. 3
Fig. 3 Principle of fringe projection profilometry.
Fig. 4
Fig. 4 Segmentation fitting of defocus kernel σ.
Fig. 5
Fig. 5 Layout of the projector kernel calibration
Fig. 6
Fig. 6 Projector defocus kernel calibration setup: (a) Calibrated projector defocus kernel-distance relationship; (b) Calibrated camera defocus kernel-distance relationship.
Fig. 7
Fig. 7 Simulation result of optimal frequency design: (a) Optimal frequency ω = 1/4rad/pixel. (b) Optimal frequency ω = 1/5rad/pixel. (c) Optimal frequency ω = 1/6rad/pixel. (d) Optimal frequency ω = 1/7rad/pixel.
Fig. 8
Fig. 8 Three different objects to be measured for the evaluation of our proposed method.
Fig. 9
Fig. 9 Defocus kernel maps for plane measurement: (a) Camera defocus kernel. (b) Projector defocus kernel. (c) Total defocus kernel of camera and projector.
Fig. 10
Fig. 10 Designed phase for plane measurement: (a) Designed phase along Up. (b) Variable period number along Up. (c) Designed phase for Vp. (d) Variable period number along Vp.
Fig. 11
Fig. 11 Illustration of the measured point cloud of the plane by uniform-frequency fringes: (a)–(c) are point clouds corresponding to nTh = 10, nTh = 20 and nTh = 30, respectively; (d)–(f) are measurement errors correspondingly.
Fig. 12
Fig. 12 Designed variable-frequency fringe pattern and point cloud of plane measured by variable-frequency fringe pattern: (a)Designed variable-frequency vertical fringe pattern; (b)Designed variable-frequency parallel fringe pattern; (c) Plane point cloud; (d) Measurement errors of plane fitting of the point cloud in (c).
Fig. 13
Fig. 13 Plane measurement comparison between uniform-frequency and variable-frequency fringes: (a)Plane measured ten times in first place; (b) Plane measured ten times in second place; (c) Plane measured ten times in third place.
Fig. 14
Fig. 14 Defocus kernel maps for sphere measurement: (a) Camera defocus kernel. (b) Projector defocus kernel. (c) Total defocus kernel of camera and projector.
Fig. 15
Fig. 15 Designed phase for sphere measurement: (a) Designed phase along Up; (b)Variable period number along Up; (c) Designed phase for Vp; (d)Variable period number along Vp.
Fig. 16
Fig. 16 Designed variable-frequency fringe pattern and point cloud of sphere measured by variable-frequency fringe pattern: (a) Designed variable-frequency vertical fringe pattern; (b) Designed variable-frequency parallel fringe pattern; (c) Sphere point cloud measured by variable-frequency; (d) Measurement errors of sphere fitting of the point cloud in (c).
Fig. 17
Fig. 17 Illustration of the measured point cloud of the sphere by uniform-frequency with different frequencies: (a)–(c) are point clouds corresponding to nTh = 10, nTh = 20 and nTh = 30, respectively; (d)–(f) are respectively measurement errors correspondingly.
Fig. 18
Fig. 18 Sphere measurement comparison between uniform-frequency fringe and variable frequency fringes: (a) Sphere measured in first place; (b) Sphere measured in second place.
Fig. 19
Fig. 19 Defocus kernel for step like plane measurement: (a) Camera defocus kernel. (b) Projector defocus kernel. (c) Total defocus kernel of camera and projector.
Fig. 20
Fig. 20 Designed phase for step like plane measurement: (a) Designed phase along Up. (b) Variable period number along Up. (c) Designed phase for Vp. (d) Variable period number along Vp.
Fig. 21
Fig. 21 Point cloud and measurement error of step like plane by uniform-frequency and variable-frequency fringes: (a) Point cloud measured by uniform-frequency nTh = 15; (b) Point cloud measured by variable-frequency; (c) Measurement errors of plane fitting of the point cloud in (a); (d) Measurement errors of step like planes fitting of the point cloud in (b).

Tables (5)

Tables Icon

Table 1 Mean values of the RMS error for plane measurement(mm)

Tables Icon

Table 2 RMS error of plane fitting on shrunk evaluated area(mm)

Tables Icon

Table 3 Mean values of the RMS error for sphere measurement(mm)

Tables Icon

Table 4 RMS errors of sphere fitting by shrinking the evaluated area(mm)

Tables Icon

Table 5 Fitting error of step plane

Equations (46)

Equations on this page are rendered with MathJax. Learn more.

ϕ ( U c , U c ) = arctan { i = 1 N I i c ( U c V c ) sin [ ( i 1 ) 2 π / N ] i = 1 N I i c ( U c V c ) cos [ ( i 1 ) 2 π / N ] } ,
ϕ ( U c , V c ) = f ( I 1 c ( U c , V c ) , I 2 c ( U c , V c ) , , I N c ( U c , V c ) ) .
Δ ϕ ( U c , V c ) = f I 1 c Δ I 1 c + f I 2 c Δ I 2 c + + f I N c Δ I N c .
I i c ( U c , V c ) = I c   + I c   cos [ ϕ ( U c , V c ) + ( i 1 ) 2 π / N ] ,
f I i c = 2 sin [ ϕ ( U c , V c ) + ( i 1 ) 2 π / N ] N I c .
| Δ ϕ | max = | i = 1 N f I c   | | Δ I | = 2 N I c   | i = 1 N sin [ ϕ ( x , y ) + ( i 1 ) / N 2 π ] | | Δ I | = M sin ϕ N I c   | Δ I | .
| Δ U p | max = | Δ ϕ | max ω = M sin ϕ N I c   1 ω | Δ I | ,
G ( U p , V p ) = 1 2 π σ 2 e U p 2 + V p 2 2 σ 2 = ( 1 2 π σ e U p 2 2 σ 2 ) ( 1 2 π σ e V p 2 2 σ 2 ) = G ( U p ) G ( V p ) ,
I i p ( U p , V p ) u = I p   + I p   cos [ ω u U p + ( i 1 ) 2 π / N ] ,
I c ( U c , V c ) = G ( U p , V p ) I p ( U p , V p ) .
( I c ( U c , V c ) ) = ( G ( U p , V p ) ) ( I p ( U p , V p ) ) = ( G ( U p ) ) ( G ( V p ) ) ( I p ( U p , V p ) ) ,
I c ( U c , V c ) u = 1 ( ( I c ( U p , V p ) u ) ) = I p   + ( G ( U p ) ) I p cos [ ω u U p + ( i 1 ) 2 π / N ] .
{ I c   = I p   I c   = I p   e σ 2 ω u   2 2
| Δ U p | max = ( M sin ϕ N I p   | Δ I | ) 1 ω e ω 2 σ 2 2 ( ω = ω u ) .
h σ ( ω ) = 1 ω e σ 2 ω 2 .
ω o p t = 1 σ ,
σ p ( u ) R p ( u ) = | D p ( u f p 1 ) | + r u v a p u + b p ,
σ c ( u ) R c ( u ) = D c s ( 1 f c 1 s 1 u ) a c ( b c 1 u ) ,
σ = σ p 2 + σ c 2 .
[ U c V c 1 ] = 1 z c [ f c u 0 U c 0 0 f c v V c 0 0 0 1 ] x c y c z c
{ u c = U c U c 0 f c u = x c z c v c = V c V c 0 f c v = y c z c .
{ u c = U p U p 0 f p u = x p z p v p = V p V p 0 f p v = y p z p ,
[ x p , y p , z p ] T = R p c [ x c , y c , z c ] T + t p c ,
{ z c = t 1 t 3 u p J u p H x c = u c z c y c = v c z c ,
Δ z c = t 3 H t 1 J ( J u p H ) Δ u p = t 3 H t 1 ( J u p H ) 2 Δ U p f p u .
Δ ( u c , v c , u p ) = Δ x c 2 + Δ y c 2 + Δ z c 2 = u c 2 + v c 2 + 1 | Δ z c | .
Δ max ( u c , v c , u p ) = k ( u c , v c , u p ) K sin ϕ h σ ( ω ) | Δ I | ,
Δ ¯ ( u p , ω ) = K sin ϕ j = 1 | V 2 V 1 | k j h σ j ( ω ) | V 2 V 1 | | Δ I | = K sin ϕ k j ¯ h σ ¯ ( ω ) | Δ I | ,
h σ ¯ 1 ( ω ) = 1 ω exp ( ω 2 2 i = 1 | V 2 V 1 | λ i σ i 2 ) h σ ¯ ( ω ) 1 ω ( i = 1 | V 2 V 1 | λ i exp ( σ i 2 ) ) ω 2 2 = h σ ¯ ( ω ) ,
1 σ ¯ 2 ω o p t ( U ^ p ) = 1 σ ¯ 1 σ ¯ 1 .
ϕ ( U ^ p ) = 0 U ^ p ω ( U p ) d U p ,
ϕ ( U ^ p ) = 0 U p l 1 σ 1 ( U p l ) d U p C 0 + j = 1 m 1 U p l + ( j 1 ) W s U p l + j W s 1 σ j d U p + + U p l + ( m 1 ) W s U ^ p 1 σ m d U p
= C 0 + j = 1 m 1 U p l + ( j 1 ) W s U p l + j W s 1 α j U p + β j d U p C m 1 + + U p l + ( m 1 ) W s U ^ p 1 α m U p + β m d U p = C m 1 + 1 α m log ( α m U ^ p + β m α m [ U p l + ( m 1 ) W s ] + β m ) ( α m 0 ) ,
ϕ ( U ^ p ) = C m 1 + U p l + ( m 1 ) W s U ^ p 1 β m d U p = C m 1 + U ^ p ( U p l + ( m 1 ) W s ) β m .
S u = r o u n d ( U p r U p l W s ) ,
I i , ϕ p ( U ^ p , V ^ p ) u = I p   + I p   cos [ ϕ ( U ^ p ) + ( i 1 ) / N 2 π ] , i = 1 , 2 , , N ,
I i , ϕ p ( U ^ p , V ^ p ) v = I p   + I p   cos [ ϕ ( V ^ p ) + ( i 1 ) / N 2 π ] , i = 1 , 2 , , N .
ϕ ˜ = arctan { i = 1 N I ϕ ( i ) sin [ 2 π ( i 1 ) / N ] i = 1 N I ϕ ( i ) cos [ 2 π ( i 1 ) / N ] } [ π , π ) ,
ϕ = { ϕ ˜ ϕ ˜ 0 ϕ ˜ + 2 π ϕ ˜ < 0 .
Q ( U ^ c , V ^ c ) = r o u n d ( 0 U ¯ p ω ( U p ) d U p ϕ 2 π ) .
ϕ ( U ^ p ) = 0 U ^ p ω ( U p ) d U p = Q ( U ^ c , V ^ c ) 2 π + ϕ ,
U ^ p ( U ^ p , V ^ c ) = [ U p l + ( m 1 ) W s + β m α m ] exp [ α m ( 2 π Q + ϕ C m 1 ) ] β m α m ;
U ^ p ( U ^ c , V ^ c ) = β m ( 2 π Q + ϕ C m 1 ) + [ U p l + ( m 1 ) W s ] .
σ p = 0.2486 z p 53.2983 .
σ c = 5.353 × 10 6 z c 3 + 0.00541 z c 2 1.7816 z c + 193.4647 .
A N G i = cos 1 ( | N i N min N i N min | ) ,

Metrics